Spatially penalized regression for dependence analysis of rare events: A study in precipitation extremes

Discovery of dependence structure between precipitation extremes and other climate variables (covariates) within a smaller spatial and temporal neighborhood is an important step in better understanding the drivers of this complex phenomenon as well as short-term prediction of extremes occurrence. Apart from the inherent spatio-temporal variability of the dependence, it is further complicated by the availability of the covariates at different vertical levels. The above problem can be split into three different sub-problems. Firstly, a spatio-temporal neighborhood of influence has to be discovered, which can be different for different locations. Secondly, the dependence structure between the precipitation extremes and the covariates has to be discovered within this neighborhood and thirdly, it has to be investigated whether this dependence structure can be exploited for any predictive power. Climate scientists have already discovered some physics-based relations between some of the covariates (e.g. temperature, relative humidity, precipitable water etc.) and precipitation extremes. We are exploring data-dependent alternatives for these problems and any possibility of incorporating the physics-based relations into the resulting data model. In particular, we used elastic net-based sparse optimization technique which solves all three problems of neighborhood discovery, covariate dependence discovery and predictive modeling and at the same time maintains the interpretability of the resulting model. Preliminary results look promising and show potential for some interesting knowledge discovery. We are currently exploring non-linear correlations and the alternatives to combine the physics-based relationships into the data model.